Question

Identify the algebraic expression is polynomial.. If so, write their degree .

$x^{2}y-2x{y}^2+\frac{2}{3}x-1,$

Answer 1

Finding whether $x^{2}y-2x{y}^2+\frac{2}{3}x-1$ is polynomial or not :

An algebraic expression containing only one variable is called a polynomial in that variable if the powers of the variable in each term are non- negative integral powers .

Thus, an algebraic expression of the form $a+bx+c{x}^2+d{x}^3+...,$ where $a,b,c,d...$are constants and $x$is a variable, is called a polynomial in the variable $x$.

Therefore, $x^{2}y-2x{y}^2+\frac{2}{3}x-1$ is a polynomial.

The greatest power of $x$ present in the polynomial is called the degree of the polynomial .

Since,the constant are $\frac{2}{3},-1,-2$ and variable are $x^{2}y,-x{y}^{2}andx$

Hence ,The degree of expression $x^{2}y-2x{y}^2+\frac{2}{3}x-1$ is $2$.